River bifurcationRiver bifurcation (from furca, fork) occurs when a river flowing in a single stream separates into two or more separate streams (called distributaries) which then continue downstream. Some rivers form complex networks of distributaries, typically in their deltas. If the streams eventually merge again or empty into the same body of water, then the bifurcation forms a river island. River bifurcation may be temporary or semi-permanent, depending on the strength of the material that is dividing the two distributaries.
StreamA stream is a continuous body of surface water flowing within the bed and banks of a channel. Depending on its location or certain characteristics, a stream may be referred to by a variety of local or regional names. Long, large streams are usually called rivers, while smaller, less voluminous and more intermittent streams are known as streamlets, brooks or creeks. The flow of a stream is controlled by three inputs – surface runoff (from precipitation or meltwater), daylighted subterranean water, and surfaced groundwater (spring water).
Bifurcation theoryBifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behavior.
River deltaA river delta is a landform shaped like a triangle, created by the deposition of sediment that is carried by a river and enters slower-moving or stagnant water. This occurs when a river enters an ocean, sea, estuary, lake, reservoir, or (more rarely) another river that cannot carry away the supplied sediment. It is so named because its triangle shape resembles the Greek letter Delta. The size and shape of a delta are controlled by the balance between watershed processes that supply sediment, and receiving basin processes that redistribute, sequester, and export that sediment.
Hopf bifurcationIn the mathematical theory of bifurcations, a Hopf bifurcation is a critical point where, as a parameter changes, a system's stability switches and a periodic solution arises. More accurately, it is a local bifurcation in which a fixed point of a dynamical system loses stability, as a pair of complex conjugate eigenvalues—of the linearization around the fixed point—crosses the complex plane imaginary axis as a parameter crosses a threshold value.
River engineeringRiver engineering is a discipline of civil engineering which studies human intervention in the course, characteristics, or flow of a river with the intention of producing some defined benefit. People have intervened in the natural course and behaviour of rivers since before recorded history—to manage the water resources, to protect against flooding, or to make passage along or across rivers easier. Since the Yuan Dynasty and Ancient Roman times, rivers have been used as a source of hydropower.
Abnormal grain growthAbnormal or discontinuous grain growth, also referred to as exaggerated or secondary recrystallisation grain growth, is a grain growth phenomenon through which certain energetically favorable grains (crystallites) grow rapidly in a matrix of finer grains resulting in a bimodal grain size distribution. In ceramic materials this phenomenon can result in the formation of elongated prismatic, acicular (needle-like) grains in a densified matrix with implications for improved fracture toughness through the impedance of crack propagation.
Period-doubling bifurcationIn dynamical systems theory, a period-doubling bifurcation occurs when a slight change in a system's parameters causes a new periodic trajectory to emerge from an existing periodic trajectory—the new one having double the period of the original. With the doubled period, it takes twice as long (or, in a discrete dynamical system, twice as many iterations) for the numerical values visited by the system to repeat themselves. A period-halving bifurcation occurs when a system switches to a new behavior with half the period of the original system.
Water qualityWater quality refers to the chemical, physical, and biological characteristics of water based on the standards of its usage. It is most frequently used by reference to a set of standards against which compliance, generally achieved through treatment of the water, can be assessed. The most common standards used to monitor and assess water quality convey the health of ecosystems, safety of human contact, extent of water pollution and condition of drinking water.
Bifurcation diagramIn mathematics, particularly in dynamical systems, a bifurcation diagram shows the values visited or approached asymptotically (fixed points, periodic orbits, or chaotic attractors) of a system as a function of a bifurcation parameter in the system. It is usual to represent stable values with a solid line and unstable values with a dotted line, although often the unstable points are omitted. Bifurcation diagrams enable the visualization of bifurcation theory.
